Study On L~1Solutions Of Multidimensional BSDEs With Uniformly Continuous Generators And Applications Of BSDEs In Insurance

In this paper, the existence and uniqueness for L1 solutions of multidimensional backward stochastic differential equations (BSDEs for short) with uniformly continu-ous generators is mainly studied, and the applications of BSDEs in insurance are also discussed, which generalizes some existing results.In Chapter 1, the background on BSDEs, research contents and some preliminaries for the following chapters are introduced.In Chapter 2, an existence and uniqueness result for L1 solutions of multidimen-sional BSDEs (See Theorem 2.3) is put forward and proved by the method of the a priori estimates and the convolution technique, where the generator g satisfies a Os-good condition in y and a α-Holder (0<α<1) continuity condition in z, and the ith component gi(t, y, z) of g only depends on the ith row of matrix z. The corresponding results in Fan-Jiang [2012b] are generalized by our work.The applications of BSDEs in insurance pricing are discussed in Chapter 3. By using the BSDEs theory, an insurance pricing BSDEs model and a reinsurance pricing BSDEs model based on investment of insurance are firstly established. Then, the pric-ing formulae is achieved by solving the BSDEs. Some demonstration analysis is also provided in this chapter.Finally, a summary and prospect of this paper are given in Chapter 4.